How do you kill zedonius in the second battle?

Patience. Don't get headstrong, and dodge his fire ball, fire pillar, and dive attacks. He's going to grab you a lot, so I would recommend using either the Eclipse Scythe, TD Sword, Vig's, or the Kusari-Gama. These ones are your best bet because he flies around a lot like a coward and they can hit him, at least every now and then. Don't waste your time with projectiles; they don't do very good damage anyways.

Ninpo isn't the best, either, but it's still very useful and in many cases crucial. Use Art of the Wind Blades as he dives to the ground (launching that annoying fire wave) and you should do some worthwhile damage while evading that attack.

Like I said, the key to beating Zedonius is patience. His attacks are powerful, he blocks a lot, and he's hard to dodge and block. That means going on the offensive = needing to heal a lot. The one weakness the Ruler of Flame has is his lack of speed, and if you can land enough damage on him he'll go down for about 3 seconds, which is the only time to go offensive. Otherwise, stay on the defense and you'll make quick work of him.

I personally use the Eclipse Scythe's aerial attacks against him: he can't grab me (since I dash around after I land and use A+X often).